The standard use in model theory is something like this. A partial type $p$ is internal to a type $q$ if there is a definable function $f$ such that any realization of $p$ is equal to $f(c_1,\dots,c_m)$ where $c_1,\dots,c_m$ are realizations of $q$.

A typical example from differential fields: Let $X$ be the set of solutions of a linear differential equation of order $n$. Then $X$ is internal to the constants. Let $a_1,\dots,a_n$ be a fundamental system of solutions. Let $f(c_1,\dots,c_n)=\sum c_ia_i$.

The standard use in model theory is something like this. A partial type $p$ is internal to a type $q$ if there is a definable function $f$ such that any realization of $p$ is equal to $f(c_1,\dots,c_m)$ where $c_1,\dots,c_m$ are realizations of $q$.

A typical example from differential fields: Let $X$ be the set of solutions of a linear differential equation of order $n$. Then $X$ is internal to the constants. Let $a_1,\dots,a_n$ be a fundamental system of solutions. Let $f(c_1,\dots,c_n)=\sum c_ia_i$. Then every element of $X$ is the image of an $n$-tuple of constants.